Multiple solutions for elliptic problem in $\mathbb{R}^N$ with critical Sobolev exponent and weight function

Existência E Multiplicidade De Soluções Para Uma Equação Elítica Quaselinear Do Tipo Kirchhoff

“…Citamos ainda dentre outros, os trabalhos de Alves et al (2005), Dai (2009), Dai e Liu (2009), Dai e Wei (2010), Alves et al (2010), Miotto (2010), Cammaroto e Vilasi (2011), Colasuonno e Pucci (2011), Sun e Tang (2011), Pei (2012, Huang et al (2013), Hssini et al (2013), Ferrara et al (2014, Miotto (2014) e Hssini et al (2015 os quais utilizam argumentos variacionais.…”

MULTIPLICIDADE DE SOLUÇÕES PARA UMA CLASSE DE PROBLEMAS QUASELINEARES CRÍTICOS EM R<SUP>N</SUP> ENVOLVENDO FUNÇÃO PESO COM MUDANÇA DE SINAL

“…First, we will show the case where p = 2. The proof is in Miotto (2010), but for the sake of completeness, we will give a sketch of the proof. Since f > 0 in the set where v ε = v y,ε > 0, it follows from the estimates obtained by Brezis e Nirenberg (1983, 1989) that…”

“…The author in Miotto (2010) treated problem (1) with p = 2, combining techniques used by Tarantello (1992) and Ambrosetti et al (2000) (see also Brown e Zhang (2003) and Wu (2008)). For p > 2, the same arguments used above in Miotto (2010) does not work any longer in direct way, mainly in the proof of the estimates of the critical level, due to lack of regularity of solutions. In order to get such estimative, we will show that the solutions of problem (1) belong in C 1,γ loc (R N \{0}).…”